# Functionalizing a Tapered Microcavity as a Gas Cell for On-Chip Mid-Infrared Absorption Spectroscopy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{4}), ethane (C

_{2}H

_{6}) and propane (C

_{3}H

_{8}) in the 3.2 $\mathsf{\mu}$$\mathrm{m}$ to 3.4 $\mathsf{\mu}$$\mathrm{m}$ wavelength range in the mid-infrared.

_{2}thin-film layers with quarter-wavelength optical thickness, while the first layer of the tapered mirror is varied linearly along the length of the filter to create the tapered cavity. The combined reflectivity of the mirrors varies between $98.4\%$ and $99.5\%$, depending on the position along the length of the filter.

_{2}layer of the tapered mirror implies a varying thickness along the length of the filter and renders the mirror reflectivity position dependent. Therefore, the combined effect of the wavelength and the layer thickness dependency causes the mirror reflectivity to vary along the length of the device. It must be noted that variations caused by wavelength dependency are negligible compared to the variations caused by the tapered SiO

_{2}layer.

_{2}layer is centered at 3.3 $\mathsf{\mu}\mathrm{m}$ as three quarter-wavelengths to create the 1.5 $\mathsf{\mu}\mathrm{m}$ level difference required for the cavity. Therefore, the physical thickness of the SiO

_{2}layer with a refractive index of ${n}_{{SiO}_{2}}=1.44$ varies from 2.46 $\mathsf{\mu}$$\mathrm{m}$ to 0.96 $\mathsf{\mu}$$\mathrm{m}$. The rest of the mirror layers are quarter-wavelength thick, calculated according to the center wavelength of 3.3 $\mathsf{\mu}\mathrm{m}$. The wideband spectral response of the LVOF is calculated with 1 $\mathsf{\mu}\mathrm{m}$ step size in the x-axis as shown in Figure 3a. The wavelength is swept from 3.2 $\mathsf{\mu}$$\mathrm{m}$ to 3.4 $\mathsf{\mu}$$\mathrm{m}$ with 10 $\mathrm{n}\mathrm{m}$ steps, where the response of the filter to the shortest wavelength is located at the onset ($x=0\text{}\mathrm{m}\mathrm{m}$). The spectrum is observed right after the bottom mirror, i.e., $z=0\text{}\mathrm{m}\mathrm{m}$ and the incidence angle is selected as $\theta =-{1.61}^{\circ}$. The variation between $24.3\%$ and $51\%$ in the peak transmittance is caused by the position-dependent mirror reflectivity. The simulated full width at half maximum (FWHM) resolution is 0.8 $\mathrm{n}\mathrm{m}$ on average.

## 3. Results and Discussion

_{2}layer of the tapered mirror is fabricated by the thermal-chemical reflow of a photoresist composed of variable distanced trenches, followed by one-to-one transfer etching [28]. The level difference of the tapered layer is increased during fabrication to account for the process variations. Thus, the spectral response in the 3.2 $\mathsf{\mu}$$\mathrm{m}$ to 3.4 $\mathsf{\mu}$$\mathrm{m}$ wavelength range is observed along a shorter part of the filter length. Figure 6 shows the top-view image of the fabricated device captured by a near-infrared camera. The 20 $\mathrm{m}\mathrm{m}$ by 20 $\mathrm{m}\mathrm{m}$ die consists of three gas-filled LVOFs with gas inlet and outlet on the sides.

_{4}fiber, the light beam is collimated by an aspheric lens package with a focal length of $f=5.95\text{}\mathrm{m}\mathrm{m}$ resulting in a light beam with a $1/{e}^{2}$ diameter of 1 $\mathrm{m}\mathrm{m}$ at a distance equal to the focal length of the lens. Measured full-angle beam divergence is 0.125${}^{\circ}$, which falls within the ${3}^{\circ}$ full-cone angle limit of the gas-filled LVOF. The collimated light beam reflects off the beam-steering mirror that is aligned at the optimum incidence angle for the given filter-detector separation. After passing through the device, the light is collected at the large-area PbSe detector, on which a 3 $\mathrm{m}\mathrm{m}$-tall and 15 $\mathsf{\mu}\mathrm{m}$-wide slit is mounted to replicate a pixel in a detector array. The combination of a large-area detector and a slit is chosen over a detector array mainly due to the limited availability of an array in the mid-infrared range. Moreover, the constant width of a pixel in such an array could be a limiting factor in characterization, where the detector pixel must be narrower than the length that corresponds to the FWHM resolution of the filter to be able to construct the transmission curve. Using such a slit enables the collection of high-resolution data thanks to its narrow width, while maximizing the light throughput due to its height. The flow of both pure sample gas and nitrogen as the infrared-inactive diluting component through the filter cavity is regulated by mass-flow controllers at a rate of $3$ $\mathrm{L}$/$\mathrm{h}$ in total.

_{2}layer. The change in the angle of reflection as the beam propagates in the cavity is still estimated by a constant slope as shown as the linear approximation curve in Figure 10. Therefore, the localized slope due to the irregularities in the taper is ignored. Moreover, the simulations are based on a single profile measurement taken along the length of the filter. However, the profile variations along the width of the filter contribute to the spectral response as well. Note that the height of the slit placed in front of the detector (3 $\mathrm{m}\mathrm{m}$) determines the width of the filter that is covered during the measurements. Furthermore, the angular alignment of the slit on the detector with respect to the filter, combined with the possible variations in profile along the width of the filter could cause widening in the transmission curves.

_{2}layer is tapered to form a tapered cavity, mirror reflectivity and transmissivity contribute to the positional shift of the curve in the x-axis as well, due to their position dependency.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Side view of the gas-filled linear variable optical filter (LVOF), composed of a flat and a tapered mirror with a tapered resonator cavity in-between.

**Figure 3.**Simulated wideband spectral response of (

**a**) the LVOF; (

**b**) LVOF with methane; (

**c**) LVOF with ethane and (

**d**) LVOF with propane.

**Figure 4.**Peak transmittance of the LVOF at 3.3 $\mathsf{\mu}\mathrm{m}$ wavelength with respect to the number of reflections in the cavity, observed at normal and oblique incidence.

**Figure 5.**Effective optical absorption path length values calculated along the length of the filter for the absorption coefficients of 0.2 ${\mathrm{m}\mathrm{m}}^{-1}$, 0.5 ${\mathrm{m}\mathrm{m}}^{-1}$ and 0.8 ${\mathrm{m}\mathrm{m}}^{-1}$ at (

**a**) normal and (

**b**) oblique incidence.

**Figure 7.**(

**a**) the illustration of a light bundle impinging on the flat mirror of the LVOF; (

**b**) transmission response of the LVOF calculated for both collimated and non-collimated light at various cone angles.

**Figure 8.**(

**a**) schematic illustration of the optical characterization setup; (

**b**) filter and detector shown in detail.

**Figure 9.**The wideband spectral response of the gas-filled LVOF with various mixtures of methane and nitrogen (

**a**) simulated using the measured profile of the mirrors and (

**b**) measured using the optical parametric oscillator (OPO) laser at the wavelengths of 3221.69 $\mathrm{n}\mathrm{m}$, 3270.75 $\mathrm{n}\mathrm{m}$, 3317.89 $\mathrm{n}\mathrm{m}$ and 3416.60 $\mathrm{n}\mathrm{m}$.

**Figure 10.**Cavity length calculated using the profile measurements of the flat and the tapered mirrors with the related linear approximation of the slope.

**Figure 11.**Measured spectral response of the gas-filled LVOF with nitrogen and ethane at the wavelengths of (

**a**) 3222 $\mathrm{n}\mathrm{m}$ and (

**b**) 3448 $\mathrm{n}\mathrm{m}$.

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**MDPI and ACS Style**

Ayerden, N.P.; Mandon, J.; Harren, F.J.M.; Wolffenbuttel, R.F.
Functionalizing a Tapered Microcavity as a Gas Cell for On-Chip Mid-Infrared Absorption Spectroscopy. *Sensors* **2017**, *17*, 2041.
https://doi.org/10.3390/s17092041

**AMA Style**

Ayerden NP, Mandon J, Harren FJM, Wolffenbuttel RF.
Functionalizing a Tapered Microcavity as a Gas Cell for On-Chip Mid-Infrared Absorption Spectroscopy. *Sensors*. 2017; 17(9):2041.
https://doi.org/10.3390/s17092041

**Chicago/Turabian Style**

Ayerden, N. Pelin, Julien Mandon, Frans J. M. Harren, and Reinoud F. Wolffenbuttel.
2017. "Functionalizing a Tapered Microcavity as a Gas Cell for On-Chip Mid-Infrared Absorption Spectroscopy" *Sensors* 17, no. 9: 2041.
https://doi.org/10.3390/s17092041